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Analysis of a semi-Lagrangian method for the spherically symmetric Vlasov-Einstein system

Published online by Cambridge University Press:  04 February 2010

Philippe Bechouche  and
Nicolas Besse
Philippe Bechouche
Affiliation:
Departamento de Matemática Aplicada Facultad de Ciencias, Universidad de Granada, Avda. Fuentenueva s/n, 18071 Granada, Spain. phbe@ugr.es
Nicolas Besse
Affiliation:
Institut de Mathématiques Elie Cartan & Institut Jean Lamour, Département Physique de la Matière et des Matériaux, Nancy-Université, Université Henri Poincaré, BP 70239, 54506 Vandœuvre-lès-Nancy Cedex, France. besse@iecn.u-nancy.fr
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Abstract

We consider the spherically symmetric Vlasov-Einstein system in the case of asymptotically flat spacetimes. From the physical point of view this system of equations can model the formation of a spherical black hole by gravitational collapse or describe the evolution of galaxies and globular clusters. We present high-order numerical schemes based on semi-Lagrangian techniques. The convergence of the solution of the discretized problem to the exact solution is proven and high-order error estimates are supplied. More precisely the metric coefficients converge in L ∞ and the statistical distribution function of the matter and its moments converge in L 2 with a rate of $\mathcal{O}$ (Δt 2 + hm /Δt), when the exact solution belongs to Hm .

Keywords

Vlasov-Einstein systemsemi-Lagrangian methodsconvergence analysisgeneral relativity
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 44 , Issue 3 , May 2010 , pp. 573 - 595
Copyright
© EDP Sciences, SMAI, 2010

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